This application relates to systems and methods for OFDM transmission.
With video traffic set to account for over 90% of all network traffic by 2012, the transport capacity of next-generation optical access/metro networks (<600 km) will migrate to 40-Gb/s or 100-Gb/s per channel in the near future. However, unlike high-speed long-haul systems (1000+ km) that can offset a high implementation cost, it is critical that technologies for future optical access/metro networks be both highly cost-efficient and flexible in order to be attractive candidates for next-generation systems.
Due to high spectral efficiency, resilience to linear dispersion, and efficient digital signal processing (DSP)-based implementation, optical orthogonal frequency division multiplexing (OFDM) has emerged as an attractive candidate for future fiber-optic systems. Moreover, optical OFDM-based Multiple Access (OFDMA) is attractive for next-generation optical access/metro systems due to its application transparency and bandwidth flexibility. To further increase spectral efficiency at ultra high-speeds with reduced optical receiver complexity and cost, polarization-multiplexed (POLMUX) OFDM transmission with direct (non-coherent) detection (POLMUX-OFDM-DD) has been proposed and demonstrated. By achieving record 40+ Gb/s data rates with simplified optical receivers, POLMUX-OFDMA with direct detection (DD) is a highly-promising technology for future fiber-based access/metro systems.
However, while POLMUX-OFDM-DD systems reduce receiver complexity compared to coherent receivers, they also increase the complexity of the required post-photodetection electronic DSP. Namely, due to direct detection, cross-polarization interference will occur in the optical receiver, which must be corrected, or equalized, in post-photodetection DSP. Unlike in POLMUX-OFDM systems with coherent detection, however, with POLMUX-OFDM-DD, the inverse of a 4×4 channel estimation matrix must be computed to do so. The computational complexity of this task alone for an M×M matrix grows as O(M3M). This means that for M=4, a single execution of the task would increase complexity by M3M=256 digital operations. Combined with the thousand-fold repetition per second needed for equalization of the cross-polarization interference, the matrix inversion alone would increase the computational complexity by ˜105 operations/second. Such an increase from one task is fundamentally prohibitive for real-time high-speed (40+ Gb/s) POLMUX-OFDM-DD systems. Moreover, equalization based on the direct matrix inversion, known as zero forcing (ZF), is known to degrade performance by enhancing noise effects. Consequently, a computationally-efficient equalization algorithm that can also remove noise enhancement is of high importance for high-speed, real-time POLMUX-OFDM-DD systems.
FIG. 1 shows a conventional POLMUX-DD-OFDM system. In FIG. 1, a POLMUX-OFDM signal is generated in the Dual-PolMux OFDM transmitter and transmitted over standard single mode fiber (SSMF). As shown in FIG. 1, the Dual-PolMux OFDM transmitter is non-adaptive since it has no information about the SSMF link quality and cannot adjust its parameters to optimize the transmission rate. At the receiver, the POLMUX-OFDM signal is split into two components by a polarization beam splitter (PBS) and direct-detected by two photo-diodes (PD). After analog-to-digital conversion (ADC), each component is processed by an OFDM receiver, and sent to the MIMO PolDeMux receiver. The DSP-based PolDeMux receiver performs equalization of the cross-polarization interference which occurs during photodetection. Specifically, using the output of the OFDM receivers, the PolDeMux receiver obtains the following model, wherein for simplicity no additive noise is assumed:
                              [                                                                                          c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    11                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    21                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    11                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    21                                                                                                                                            c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    11                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    21                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    11                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    21                                                                                                                                            c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    12                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    22                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    12                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    22                                                                                                                                            C                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    12                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    22                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    12                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    22                                                                                ]                          ︸                      PolMux            ⁢                                                  ⁢            channel            ⁢                                                  ⁢            estimation            ⁢                                                  ⁢            matrix                              ×                        [                                                                      X                  i                                                                                                      X                                      n                    -                    i                    +                    1                                                                                                                        Y                  i                                                                                                      Y                                      n                    -                    i                    +                    1                                                                                ]                          ︸                      Tx            ⁢                                                  ⁢            signals                                =                  [                                                            X                i                ′                                                                                        X                                  n                  -                  i                  +                  1                                ′                                                                                        Y                i                ′                                                                                        Y                                  n                  -                  i                  +                  1                                ′                                                    ]                    ︸                  Re          ⁢                                          ⁢          signals                                PolMux      ⁢                          ⁢      channel      ⁢                          ⁢      estimation      ⁢                          ⁢      matrix        ;          Tx      =      transmitted        ;          Re      =      received      
In the PolMux channel estimation matrix, the coefficients a and b are the power splitting ratios caused by polarization rotation, and c is decided by the power difference between the optical carrier and the OFDM signal. Moreover, no matrix structure is apparent from the PolMux matrix formulation. Next, the PolDeMux receiver of FIG. 1 computes the inverse of the channel estimation matrix, i.e. the PolDeMux matrix, and performs the equalization by directly multiplying the inverse matrix with the received (Re) signals. This multiplication step is also known as zero forcing (ZF). It is also noted that no matrix structure is apparent from the PolDeMux matrix formulation below:
                              [                                                                                          c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    11                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    21                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    11                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    21                                                                                                                                            c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    11                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    21                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      b                    11                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        1                                                                              ⁢                                      a                    21                                                                                                                                            c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    12                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    22                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    12                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    22                                                                                                                                            C                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    12                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    22                                                                                                                    c                                          X                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      b                    12                                                                                                                    c                                          Y                      ,                                              ch                        ⁢                                                                                                  ⁢                        2                                                                              ⁢                                      a                    22                                                                                ]                          ︸                      PolDeMux            ⁢                                                  ⁢            matrix                                      -        1              ×                  [                                                            X                i                ′                                                                                        X                                  n                  -                  i                  +                  1                                ′                                                                                        Y                i                ′                                                                                        Y                                  n                  -                  i                  +                  1                                ′                                                    ]                    ︸                  Re          ⁢                                          ⁢          signals                      =            [                                                  X              i                                                                          X                              n                -                i                +                1                                                                                        Y              i                                                                          Y                              n                -                i                +                1                                                        ]              ︸              Tx        ⁢                                  ⁢        signals            
For a M×M=4×4 matrix with no apparent structure, a single PolDeMux matrix computation via direct inversion of the channel estimation matrix would increase the computational complexity by M3M=256 digital operations. Combined with the thousand-fold repetition per second needed for equalization of the cross-polarization interference, the matrix inversion alone would increase the computational complexity by about 105 operations/second, which is fundamentally prohibitive for real-time 40+ Gb/s POLMUX-OFDM-DD systems. Moreover, in practice equalization based on direct multiplication of the PolDeMux matrix with the received (Re) signals, known as zero forcing (ZF), degrades performance by enhancing noise effects.
Another POLMUX-OFDM-DD system solves the cross-polarization interference problem through optical rather than electronic processing. Namely, at the receiver, the POLMUX-OFDM signal is split into two components, and a sharp optical filter is used to remove the carrier in one polarization. The cross-polarization interference is thus removed and DSP-based equalization is not needed. However, this approach increases the optical receiver complexity, since two very sharp, costly optical filters must be used. It also incurs a prohibitive 10+ dB penalty in the required optical signal to noise ratio (OSNR), compared to the system of FIG. 1.